Consider handwriting your letter. Handwritten letters are often seen as less threatening by homeowners and may get better results than typewritten ones.
Keep the letter short, meaning one page, ideally no more than three paragraphs. In the first paragraph, gently remind the homeowner that he has fallen behind on his mortgage payments and inform him that you would like to help him keep a foreclosure off his credit records by purchasing his home.
Restate your purpose in a different way in the second paragraph. You might include a story of how you helped another homeowner avoid foreclosure by purchasing her home, and, if possible, include a testimonial from a past homeowner.
In the third paragraph, explicitly invite the reader to contact you, and outline your plans to follow up if you do not hear from him.